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What is the $n$ th term formula for $96,-24,6$ ?

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Full solution

Q. What is the

n

th term formula for

96,-24,6

?

Identify pattern and calculate ratio: Identify the pattern in the sequence: $96$ , $-24$ , $6$ . Calculate the common ratio by dividing the second term by the first term and the third term by the second term. $\newline$ $-24 / 96 = -1/4$ $\newline$ $6 / -24 = -1/4$
Confirm sequence is geometric: Confirm the sequence is geometric since the ratio between consecutive terms is constant. The common ratio $r$ is $-\frac{1}{4}$ .
Write nth term formula: Write the formula for the nth term of a geometric sequence: $a_n = a \cdot r^{(n-1)}$ , where $a$ is the first term and $r$ is the common ratio. $\newline$ $a = 96$ , $r = -\frac{1}{4}$
Substitute values into formula: Substitute the values of $a$ and $r$ into the formula to get the nth term formula. $a_n = 96 \times \left(-\frac{1}{4}\right)^{(n-1)}$

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